A need for risk management decisions arises in a broad range of technological, industrial, and financial areas. Typical examples include operation of manufacturing, storage, and transportation facilities in an industrial logistics system, control of product mix at a factory, deployment of industrial equipment, electrical engineering and mechanical engineering problems, inventory control, advertising campaign management in a marketing program, and management of a portfolio of financial assets, to name just a few.
As an example, consider the problem of efficient lighting in a commercial facility. The facility owner has to provide the required lighting conditions in the building. He would like to install state-of-the-art lighting systems and controls in order to curb energy consumption at this facility. The state-of-the-art equipment commands a premium price, mitigated however by rebate incentives from the local utility company. At the same time, the owner would like to minimize the cost of the lighting devices that are necessary to provide the required lighting conditions.
In this example, the owner calculates the operating costs of lighting the facility with different types of devices, based upon data provided by the manufacturers. These data usually correspond to power factor at the facility being equal to 1.0. Real world conditions introduce a variability of power distribution to that facility that reduces the power factor and affects the operation of the selected equipment and, therefore, its operating costs. Such conditions induce a consideration of auxiliary devices that restore the power factor at the facility to unity.
The risk management decision in the facility owner's problem is to find a combination of the quantity and quality of lighting devices, controls, and auxiliary devices that minimizes the payback period but still affords protection from the twofold risks of both exceeding the planned operating costs and underachieving the desired lighting conditions. The decision should contain these risks within some acceptable limits.
To demonstrate the universality of the need for risk management decisions, consider next a problem of efficient distribution of products by an industrial manufacturing company. The distribution system starts with the company factories that manufacture the products and ends with buyers (such as wholesalers) who order the products. The system includes a network of distribution centers and warehouses, as well as transportation facilities to move the products. All of these may belong to the company, or may simply be used by it. All facilities of the system (namely, the factories, the distribution centers, the warehouses, and the transportation vehicles) are characterized by their production, throughput, or storage capacities. Similarly, use of all these facilities invokes their associated costs. If the distribution system is not limited to a single country, costs and prices may need to be expressed in different currencies. Manufacturing, transportation, loading and unloading, and handling the products at warehouses--all of these procedures require resources and time.
Demand depends on product prices which, in turn, may be related to cumulative product costs at the buyers' locations. It also depends on the behavior of competitors, which is determined partly by the company's own pricing and other policies, and partly on other factors, largely unknown.
Any inability to meet the buyers' demand, and to do it on time, involves explicit or implicit economic penalties. Similarly, penalties arise if the company procures work force, equipment, and materials to meet its planned production targets, and then has to change its plans, causing mismatches.
The values of all parameters of the distribution system, including its technologies, the needed production and transportation time, the required resources and capacities, demand, prices and costs, currency conversion rates, and penalties (especially implicit penalties), are not known exactly. They may also change over time. The values for these parameters can only be estimated or forecast. The risk management part of the efficient distribution problem is to find a combination of technologies, production targets, inventory levels, and transportation flow at all stages of the distribution system during the planning period, as well as of product selling prices and levels of demand to be satisfied, so that no production, warehousing, or transportation capacity constraints are exceeded and total profits are maximized, while the risks of insufficient profits or losses, penalties, foreign exchange rate changes, or unmet demand and broken schedules are kept within acceptable limits.
Finally, let us consider a financial portfolio management problem. For simplicity, assume that the portfolio may include only fixed income securities of different maturities but of one general type, such as bonds issued by the United States Treasury. The portfolio does not include corporate and municipal bonds, stocks, financial instruments in currencies other than U.S. dollars, mortgage-based securities, or derivative financial instruments, such as options.
In this last example, the portfolio manager has exact data about the composition of his portfolio, that is, about the face value of portfolio bonds, by issues. The manager also knows all characteristics of each existing Treasury bond issue, both present and not present in the current portfolio. These characteristics include the issue's date of maturity, coupon or discount rate, the schedule of coupon payments, the coupon interest that has accrued on the issue from the time of the last coupon payment, the transaction costs on acquiring or selling the bond, callability, and the availability of the issue for purchase.
In this example, the manager also knows the latest bond market quotes on bid and ask prices for all existing Treasury issues, although these quotes may differ from the real execution prices of bond trading. This difference may exist even if the bond is traded (purchased or sold) at this very moment, especially for bonds not actively traded in the market. However, both the bid and ask quotes and the execution prices for each bond issue depend upon the supply/demand relationship for that issue, which changes all the time. Therefore, if a bond is purchased or sold not immediately but later, this relationship may change drastically, entailing the corresponding price changes. For any time in the future, the portfolio manager does not know in what direction and how much prices will change for any issue. Moreover, changing bond prices affect not only new trades: the worth of the whole portfolio is regularly re-evaluated (marked-to-market) at current prices.
In this example, the portfolio manager wants to maximize portfolio returns. However, he also has to carry out certain obligations to the portfolio owners (investors). Perhaps the most important obligation is to make scheduled payments to investors--either some contractually specified amounts, amounts that stand for the returns on investment and repayment of the investment principal, or amounts that symbolically represent advances on the investment returns that are expected in the future.
Besides these payments, the portfolio will have in the future some other cash inflows and outflows. The inflows are mostly new investments in the portfolio, coupon payments from the Treasury on the portfolio bonds, and the principals of the portfolio bonds that have matured. The main outflows are the withdrawals by the investors from the portfolio and the administrative costs of portfolio management. While the coupon payments fully depend on the composition of the portfolio and the management costs can be anticipated with sufficient accuracy, both the new portfolio investments and portfolio withdrawals can at best be "educated guesses."
The portfolio can trade bonds, i.e., sell the bonds currently in the portfolio and, using these funds together with new inflows, purchase some other bonds.
The permitted portfolio trading activities are restricted by a number of laws, rules and constraints of fiduciary, regulatory, tax, and other origin. There may be constraints on borrowing, margin trading and other leveraging of the portfolio funds, short sales, and so on. One of the main constraints is a fiduciary requirement that commonly obliges the manager to preserve the principal capital of the portfolio, that is, to protect the portfolio against unacceptable risks.
The portfolio manager can base his portfolio decisions either solely on the latest bond market quotes which he knows, or on a combination of these quotes and future bond prices that can be expected for some moment of time yet to come.
The risk management problem of the portfolio manager is to find a planned combination of bond trades so that all constraints on the portfolio activities are met and the portfolio returns are maximized, while the portfolio funds are protected against losses that would exceed the acceptable risk limits.
These three examples demonstrate the extreme complexity of making risk management decisions. Still, these are relatively simple situations--real life decision-making in financial and industrial business organizations can be much more complicated. For instance, the financial portfolio in the last example could include not only Treasury bonds, but also corporate and municipal bonds, stocks, futures, options, financial instruments in other currencies, and other types of securities.
It should be noted that the risk management problems discussed above are real physical problems arising in real physical systems. (A portfolio of fixed income securities is also a physical system--a set of physical bonds.) While it is true that this invention represents significant quantitative aspects of these physical problems by mathematical models, the purpose of these models is to make decisions about target values which are then used in the physical world to construct or operate physical systems. Typical prior art examples of such mathematical models for making decisions about physical systems are the use of linear programming (LP) for efficient resource allocation or for optimizing system operational parameters, the use of scenario optimization for the management of a portfolio of financial options, and the use of mathematical equations to construct radio antennas or to control rubber-molding operations.
Moreover, the mathematical models used in this invention are, as a rule, too complicated for application in reasonable time without a computer. Therefore, their use involves changing the physical condition of the computer memory, thus virtually creating a new state of the computer.
To exercise risk management, it is first necessary to define "risk."
Every decision in any of the areas listed above, such as electrical engineering, industrial logistics, and portfolio management, involves, on the one hand, a specific allocation of resources and, on the other hand, specific outcomes from different activities of the physical system. These results may be as diverse as costs or profits, returns on financial portfolios, quality of products, the composition of product mix, consumption of electricity, penalties for broken schedules or unsatisfied demand, or the amount and chemical composition of waste water. The values of some of these results are of special concern to decision-makers (DMs), who consider such results undesirable or even potentially dangerous and want them either to stay within some boundary limits (which may or may not be known in advance), or to be as low or as high as possible. The systems activities that are subject to special concern will be called "risk-related activities."
Outcomes in risk-related activities depend both on the targets to be achieved and on the allocation of resources within the physical system. In general, it is this dependency that is described by a mathematical model. As a rule, the parameter values of the dependency relationship in the system, or of the mathematical model, are not known with certainty and can, at best, be estimated or forecast, and often just guessed. Even if they are forecast, it is still hardly ever, if at all, possible to obtain a reliable forecast, especially for the long term. The consequences of a decision about the allocation of resources in a physical system are, therefore, uncertain and involve the possibility of unexpected and, possibly, undesirable or even dangerous outcomes.
"Risk" is defined here as a magnitude of outcome levels of undesirable or potentially dangerous activities that have fallen outside the relevant boundary limits. Risk management, then, is the capability to estimate, to avoid, to control or to reduce the extent of such occasions and reduce the probability of their occurrence. "Risk" can be defined in many ways, both absolute and relative, and this invention can be applied in the framework of any of these definitions. The exact definition of risk is here irrelevant, so, for simplicity, only one definition is used.
To understand the need for the present invention, consider the current state-of-the-art both in the general is area of decision-making and, specifically, in risk management.
Roughly, from the time the computer era began--that is, in the late 1940s and early 1950s--great advances were made in two fields important to decision-making: Operations Research/Management Science (OR/MS) and Decision Science (DS). OR/MS primarily deals with optimization models, while DS analyzes alternative strategies under uncertainty and selects one candidate strategy over all others.
A rational, natural and customary way to make a decision is to recognize the uncertainty of the future and the lack of knowledge about the present, to represent the uncertainty and lack of knowledge through scenarios, and to consider the outcomes--possibly in many activities--under each scenario, given a course of action or strategy. Arranging information about these outcomes into an "outcome matrix" is a good technique for systematic analysis of the data. This is the basic approach of classical DS, which starts from an outcome matrix, or, more specifically, often from a "payoff matrix"--a special case where all outcomes are quantified and are of the same type, such as profit.
However, this assumes that scenarios, candidate strategies, and "strategy versus scenario" outcomes are specified beforehand. Thus, classical DS in effect is "passive"--it withdraws itself from tasks that constitute 95 to 99 percent, or even more, of the total effort. Instead of addressing the whole real world problem of making a decision, DS limits itself to the last, and often the easiest, part of the process.
In contrast, OR/MS uses "active" optimization models. These models address the main part of the decision-making problem not covered by DS: they formulate a plan or a strategy. Using mathematical equations and inequalities, the models define a region of feasible solutions (i.e., solutions that do not violate those equations and inequalities) and find in that region a solution that is "the best" from the point of view of one or more criteria of optimality.
The most widely used optimization model is an LP model. It is also the basis for and a major component of all other more sophisticated mathematical programming models, such as integer or non-linear programming models. It defines a set of interrelated activities and a set of constraints on the level of each activity, as well as on the levels of some specified linear functions of these activities. The LP model also defines the "objective function" as the total sum of the net benefits (benefits minus expenses) of activities, which also is a linear function of activity levels. The solution of an LP model is based on a single criterion: finding the allocation of resources to maximize the value of the objective function. One method of solving an LP model is described by U.S. Pat. No. 4,744,026 to Robert J. Vanderbei, U.S. Pat. No. 4,744,027 to David A. Bayer et al., and U.S. Pat. No. 4,744,028 to Narendra K. Karmarkar, all issued May 10, 1988.
When applied correctly, LP models have many valuable advantages. The models can integrate, connect, coordinate, balance, and jointly analyze different factors, operations, and territorial or functional parts of a physical system. They can find hidden opportunities for improvement and are easy to set up, although this simplicity can sometimes be very deceptive. They can also derive plans from the initial data, without the need of losing time and effort on intermediate analyses, and thus increase the speed of decision-making.
LP models became invaluable tools for dealing with "closed" decision-making problems, problems that exclude any significant deviations from the status quo in important decisions. In the petroleum industry, which began to apply LP in the late 1940s, mathematical programming concepts penetrated all facets of short-term business planning, from supply, distribution and refinery planning to product blending and process control. Scheduling of Air Force planes was a triumphal application of sophisticated, large-scale integer LP models during the 1991 Gulf War.
Conventional optimization techniques have never been successful, however, in dealing with "open" problems that predominate in long-term and strategic planning. This is because prudence and moderation, the two crucial components of mature decision-making and risk management, are not among the advantages of optimization models. LP models seek extremes and are stopped only by such model constraints as equations or inequalities. Even a minuscule alteration of input data, well within the margin of possible error, may cause a change of solution. Moreover, the solution always switches from one extreme to another, so that the resulting change can be disproportionately large. Therefore, solutions of LP models are inherently unstable; they introduce an additional risk component of their own.
Instability of solutions causes three major difficulties in applying such models. The first such difficulty comes from uncertainty. A model may provide valid results only if the model data are sufficiently accurate (which means the modeler must have adequate knowledge of both the present and the future), or if the major decisions in the optimal solution remain sufficiently stable as data varies regarding the possible actions and their consequences. Second, LP models have a simplistic, well defined, one-dimensional goal, while the DMs' goals usually are more diverse, conflicting, and ambiguous. Third, by definition, the models are incomplete and they may omit important factors, considerations, and constraints, such as long-term considerations in a short-term model.
In other words, LP models fully confirm an observation of Oscar Morgenstern ("On the Accuracy of Economic Observations," Princeton University Press, 1950, p. 45) that ". . . every type of numerical observation, based upon a mathematically formulated model, imposes restrictions upon the data. If these restrictions cannot be met, the operations become impossible, even if the underlying model should be free from objections."
Remedies have been proposed to deal with some of these drawbacks. For example, stochastic programming (SP), an important mathematical programming extension of LP, is intended to deal with uncertainty. To a certain degree, SP performs this function, but it offers only an implicit and limited protection against risk attendant to uncertainty. Its risk protection is valid only in a statistical sense: if its optimal solution is repeatedly implemented a very large number of times, it will eventually prove the best. However, with a few exceptions, the decision-making situations are either unique and non-repetitive or are repeated only a small number of times. If a harmful or adverse situation happens during one of those times, the losses resulting from the "optimal" decision may never be recouped.
Also important, SP does not offer choices to the decision-makers: it constructs a single solution and declares it to be the optimum. SP therefore deprives them of enormous advantages coming from the use of outcome and regret matrices and DS criteria.
However, the crucial point is that SP usually is simply inappropriate as a basis for making complex decisions in the relevant fields. In "Risk, Uncertainty and Profit," by F. H. Knight, University of Chicago Press, 1921, a clear distinction is made between "insurable risk" and "non-insurable uncertainty." In that approach, insurable risk is said to exist when the probabilities of outcomes are known exactly and are derived on an objective basis; that is, they are calculable on the basis of relative frequencies or similar data. Non-insurable uncertainty exists in the absence of objective and known probabilities.
At the same time, probabilities are considered to be calculable and adequate only for "repetitive phenomena of a standardized variety such as occur in games of chance, in actuarial science, in genetics, and in statistical mechanics." ("Decision Analysis--Introductory Lectures on Choice under Uncertainty" by Howard Raiffa, Addison Wesley, 1970, p. 274). In contrast, the decision-making problems to be addressed by SP deal with complex economic, financial, technical and social phenomena, which, as indicated above, are non-repetitive. At best, the probabilities related to these phenomena include subjective judgments and more or less educated guesses. In these problems, probabilities are the least reliable part of the input data.
Recognizing this need in probabilities of future events, a leading practitioner of SP states, for instance, in the U.S. Pat. No. 5,148,365 to Ron S. Dembo, issued Sep. 15, 1992, that "For those of skill in the art of portfolio management, the probability of the various scenarios can be guesstimated with reasonable accuracy based on experience" (column 8, lines 56-59). Notably, the author does not even mention objective probabilities which, as indicated above, are the precondition for proper applications of SP. He would be quite satisfied with the "guesstimated" probabilities, subjectively assumed by the portfolio managers.
However, even these lowered data demands cannot be met. Those "of skill in the art of portfolio management" disagree with the author's high evaluation of their capabilities and consider it to be little but wishful thinking. A leading financial forecaster writes: "To be sure, most forecasters' expectations do not work out at all. For instance, in June 1990, 88% of economists predicted continued economic expansion for at least a year. A month later, the worst recession in a decade began. As merely the latest example, a June 1994 survey of 29 of the country's most influential money managers showed that all of them expected the long bond yield to remain below 8% during the rest of last year. It was above 8% three months later. Evidence of the failure of conventional forecasting methods is more than anecdotal. According to The Wall Street Journal, a study of its own surveys since 1982 of the country's top economists reveals that in the aggregate, these acknowledged experts predicted accurately the direction (forget the extent) of interest rates only 25% of the time, which is half the success rate that would be produced purely by guessing." (Robert R. Prechter, "At the Crest of the Tidal Wave," New Classics Library, 1995, pp. 19-20). The latest surveys provide similar results. (The Wall Street Journal, Aug. 6, 1996, p. A15).
Moreover, if the applications of SP are controversial even when they involve just the insurable risk, because the "optimal" strategies do not sufficiently protect from risk, then, under uncertainty, when the objective probabilities are not known, this method becomes even more controversial. Therefore the SP procedure has to be based on a combination of two implicit premises. The first assumes that there exists an objective optimum under uncertainty, that it can be found by objective methods, and that it is just a matter of technique to find that optimum--namely, a matter of applying the correct model and getting correct data. The first premise also assumes that these techniques have been sufficiently attained in modeling and solving the problem under consideration. The second premise concedes that the optimum may indeed be subject to qualifications, such as the personal risk attitude and subjective preferences of the decision-maker, but assumes that these still can be incorporated into the SP model on the basis, say, of prior observations of the DMs' behavior and attitude, and that, again, these requirements are met in the problem under consideration.
The first assumption has been proven wrong. Both the authoritative "Games and Decisions" by R. Duncan Luce and Howard Raiffa, John Wiley & Sons, 1957, pp. 274-303 and 324-326, and later literature, such as "Decision Making under Risk and Uncertainty: New Models and Empirical Findings" ed. by John Geweke, Kluwer Academic Publishers, Dordrecht, the Netherlands, 1992, pp. 1-10, show that, even in the simplest case of a two-dimensional payoff matrix and a single decision outcome to be considered, such as profit, there are several DS criteria for decision-making under uncertainty--that is, methods for comparing and selecting strategies. (For instance, DMs can base their choice on the average profit, the best case profit, the worst case profit, and some combination of the above.) None of the known or even conceivable criteria of DS is perfect or "the best." Each has faults, such as violations of transitivity, that are revealed under some specific conditions. Thus, even in the simplest case, it is impossible to make the best decision under uncertainty in a general, unique, objective, and theoretically correct manner.
The second assumption is unrealistic, at least in the foreseeable future. As shown, for example, in the above cited "Decision Making under Risk and Uncertainty: New Models and Empirical Findings" pp. 11-16, the existing theories of personal choice under uncertainty, such as the expected utility theory, are still evolving. They cannot yet deal successfully even with some quite simple but paradoxical decision-making situations. If and when this process successfully ends and some comprehensive and consistent decision theory, both normative and descriptive, becomes a reality, its "attitude extracting" procedures still are likely to be lengthy, cumbersome, imprecise, and impractical, not suitable for real life decision-making, especially in complex business situations that require reasonably quick decisions. (The expected utility theory lays claims only to normative correctness but not to a good descriptive characterization of choice under risk and uncertainty. Therefore, it is doubtful that the theory can provide a satisfactory "attitude extracting.")
The "robust optimization" (RO) approach described, for instance, in "Robust Optimization of Large-Scale Systems" by J. M. Mulvey, R. J Vanderbei and S. A. Zenios, Operations Research, v. 43 (1995), No. 2, pp. 264-281, is an extension of SP and has some advantages over SP: it allows solutions that are relatively stable (that is, the optimal solutions under different scenarios remain closer to each other than under SP). Also, RO is multicriterial and allows tradeoffs between several criteria of optimality. However, similarly to SP, RO still relies on scenario probabilities being objectively known. (In the quoted article, the authors circumvent this crucial issue by simply mentioning, in passing, on p. 265 "the probability of the scenario." They do not explain how they succeeded in obtaining these probabilities and whether these are objective or not.) Moreover, even if these unrealistic expectations are met, RO would again offer only long run, "statistical" protection from risk, while its short-term results may be disastrous. Although, by changing the weights of different criteria, RO can form several strategies, it neither constructs payoff or outcome matrices nor applies them for comparison and selection of the best strategy. Also, RO does not use clustering and therefore has to solve models with enormous numbers of scenarios. Finally, too much importance is attached to meeting the initial constraints of the model (see later).
All above considerations about OR/MS and its tools refer to the first part of the decision-making process, namely, to the formation of candidate strategies. As for the second part (selection of a strategy), this is the province of DS. It was indicated above that there are several DS criteria for decision-making under uncertainty. Most of them are based on the "strategy versus scenario" payoff values for a strategy--either on individual values, such as the best payoff and the worst payoff of a strategy, or on values derived from individual payoffs, such as the average payoff. Three best, most comprehensive and sophisticated criteria of payoff type are the optimism-pessimism index (OP) criterion, the partial ignorance (PI) criterion, and the modified insufficient reason (IR) criterion. These three criteria, which are previously known, provide the basis for new methods of this invention.
All three are "synthetic" criteria, which means that they are quite general and include as special cases other, simpler criteria. For instance, both minimax and maximin payoffs are special cases of all three criteria, the expected payoff is a special case of the PI criterion, etc. The synthetic criteria perform an extremely important role: they minimize the negative impact of absence or lack of knowledge about probabilities of future events and their combinations (scenarios).
As mentioned before, probabilities are the least reliable part of input data, and decision analysis under risk and uncertainty cannot therefore generally dispense with subjective judgments, including judgments on probabilities. The goal is to minimize both the impact of these judgments and the effort required to form them. It is especially important to arrange the introduction and use of probabilities and other judgments in a manner least detrimental to successful decision-making, which means to postpone their use until the latest possible stage of analysis.
Fortunately, probabilities do not have to be used at the initial stages of the analysis, as is done in SP, decision tree methods, and so on. They also can be compressed into a very few parameters that estimate the overall degree of uncertainty. Furthermore, data requirements can be made less stringent by allowing the values of these parameters to fall within broad intervals, rather than correspond to a single value. Synthetic criteria meet all these requirements.
All new methods are also synthetic and therefore have the same advantages. However, these methods additionally combine OP, PI and IR with the concept of "regret" introduced into Decision Science by Savage in "The theory of statistical decision," Journal of the American Statistical Association, 46 (1951), pp. 55-67. Regret is basically a cost of uncertainty; it is derived from the payoff matrix and characterizes the risk, or regret, or opportunity lost because of choosing a wrong strategy. Regret may also be defined as the potential for reducing risk by switching strategies. See calculation of regret by Eq. (7). In some special connotations, but not in this invention, "regret" is defined as the difference between a given benchmark, such as the performance of the stock market, and the actual or projected results. In previous state-of-the-art Decision Science methods, regret has been used only in simple non-synthetic criteria, such as average regret or minimax regret (see, for instance, J. R. Buck, "Economic Risk Decisions in Engineering and Management," Iowa State University Press, 1989, pp. 313-334). To the best of my knowledge, the comprehensive OP, PI and IR criteria have not been applied to regret; it is done for the first time in this invention.
In addition, the new regret-based synthetic methods naturally give rise to decision formulas and graphs that use and expand the concept of "efficient frontier" (see later). The proposed new methods are invaluable for finding desirable limits on tightening the discretionary constraints.
A crucial difficulty in applying DS is that none of strategy selection criteria is "the best" under all circumstances. This opens the way to combining criteria--another method of this invention.
The need to deal jointly with the totality of complicated decision-making issues such as uncertainty, the multiple criteria involved in real world decision-making, and the incompleteness of mathematical models, creates additional difficulties. Especially crucial is incompleteness: it cannot be eliminated in principle, since the only complete model of a reality is the reality itself.
This analysis shows that both general approaches to decision-making (OR/MS and DS) have serious flaws if used as mutually exclusive tools, as is the current practice. Let us see how these general considerations are reflected in the specific field of risk management.
Both the theory and practice of risk management are most advanced in the financial industry, therefore we begin our survey there, although the issues and techniques that are specific to managing portfolio risks are not directly addressed in this patent application.
Modern Portfolio Theory constructs the efficient frontier--the risk/return curve, which defines a portfolio with the highest expected return for a given level of risk, or the lowest level of risk for a given level of expected return. In other words, it attempts to "optimize" a portfolio, to find the best tradeoff between expected return and expected risk. What is "the best" is determined by the subjective risk attitude of the decision-maker. However, in practice this approach is "passive": it does not form portfolios but ranks only "external" portfolios that are developed outside the system. Moreover, the weakest link of this approach is its inability to evaluate and manage risk sufficiently well. Depending on market conditions, the forecast levels of risk may prove to be good or bad approximations of reality.
Until the early 1980s, risk management in financial institutions was mainly limited to the use of Asset/Liability Models (ALM). That methodology estimates future earnings under a number of probable scenarios of economic and financial conditions, projects future cash flows for one or more candidate investment strategies, derives final assets and liabilities resulting from each strategy under each scenario, and presents the estimated returns for all "strategy versus scenario" combinations in the format of a payoff matrix. ALM thus follows the approach of DS, but its implementation has serious flaws.
ALM was primarily intended for such institutions as commercial banks, where both assets and liabilities were relatively illiquid and were priced on an accrual basis. ALM is based, however, upon a false assumption that gains or losses occur when they accrue. To find out returns, ALM needs simulation over long periods, until most portfolio transactions mature. Trading items, which must be marked-to-market, are treated separately, and it is difficult to arrange hedging between trading and accrual items. For that purpose, "proxy values" (that is, approximations to market values) have to be estimated for accrual items. ALM also has other faults. Again, one of these is that ALM is passive--it provides no means for devising a good investment strategy and evaluates only "external" candidate portfolios. A second fault is that ALM is not capable of dealing with a large number of scenarios that might be needed because long-term scenarios are not accurate. The accumulation of all these faults is worrisome.
Unfortunately, during the past two decades several trends have evolved that made risk management in finance both more difficult and more necessary. Some of the most important of these trends are:
(a) Securitization of financial instruments, increase of their liquidity, wide use of more volatile instruments, such as derivatives and especially options, and moving from accrual accounting to frequent revaluation and marking-to-market of positions; PA1 (b) Increased volatility of financial markets, which is due to their globalization, advances in information technology, and growth of mutual funds, especially those specializing in emerging markets; PA1 (c) Increased trading, and especially the institutional trading for an institution's own account; and PA1 (d) Emphasis on performance, which as a rule can be improved only by assuming higher risks, that sometimes lead to rogue trading, fraud, and eventual financial disasters.
These trends cause concern about risk control among both the institutional managers and regulators. Two risk evaluation methodologies have been developed to meet these concerns. Value-at-Risk (VAR) considers risk that arises from random market movements, while Stress Testing deals with risk of the worst-case scenarios. Both methods have their advantages and disadvantages, and they are best applicable under different circumstances.
The VAR method assumes that rate and price movements of financial instruments can be described in a statistical fashion. If VAR is applied at times when this assumption is correct and the markets are statistically stable, the method provides an estimate of the loss that is expected to occur no more than, say, 5 percent of the time.
However, VAR depends heavily on estimates of volatilities and correlations that are derived either from historical data or from the values "implied" in current market prices. The trouble is that when a market collapses or makes a sharp move, that is, when we really need the risk control method to work, all these estimates become irrelevant, because actual volatilities greatly exceed the estimated values--by at least several multiples.
The Stress Testing method uses defined scenarios, including those for unstable markets. The scenarios can be simulated on the basis of both market conditions for selected periods in the past and "educated guesses." This method provides more information of the expected portfolio performance, but it is computationally demanding even for a sharply restricted number of scenarios.
These two methods can be used in combination, benefiting from the advantages of each. Their joint use does not overcome, however, their common fault: both methods are "passive" in that they do not necessarily generate good portfolios but rather only evaluate portfolios constructed elsewhere. Both methods, and especially their combination, can be used as a prelude to "optimizing" portfolios, as defined above.
There are attempts to provide a combination of portfolio optimization with risk management by SP. The trouble with these attempts is that SP protects from risk (and only from "insurable risk") only in a stable market, where historical statistical parameters are valid.
To sum up, no methods used in portfolio management are quite satisfactory or provide good risk management.
Outside the finance industry, both the theory and practice of risk management are much less advanced. A number of large companies follow the approach of scenario planning, which can serve as a foundation to risk management. As currently used, however, this methodology as a rule is wrongly focused on the definition of scenarios, rather than on rigorous development of candidate strategies, and especially compromise strategies.
At the same time, the business world has become more volatile. Uncertainty has become the rule rather than exception, and it too often brings unpleasant surprises. As in finance, this makes risk management both more difficult and more necessary.
A common factor in all current practice is that, when dealing with multiple-parameter physical systems, effective risk management escalates quickly in complexity until it is literally beyond the capacity of the human mind to handle on any basis other than that of an educated guess or a "rule of thumb." The existing computational approaches are also inadequate. Moreover, many of them, such as LP models, increase risk by adding a risk element of their own. There is, therefore, a real and continuing need for tools that will aid in valid risk management.